We say that most bases are metal oxides and hydroxides, so an example of a base that is not ana oxide or hydroxide would be aqueous ammonia NH3(aq)?
Yes, although what is a base and/or acid depends upon which definition you wish to use. Aqueous NH3 PRODUCES OH^-.
NH3(aq) ==> NH4^+ + OH^-. One definition of an acid is something which produces H^+ but Lewis acids can be a metal ion.